plumiLimits and L'Hospital's rule: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.2 Limits and L'Hospital's rule, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 7 questions on Limits and L'Hospital's rule, as a list
- June 2025, Further Pure 1, Q4 (8 marks): y x 15 2e (a) Show that d d e e e 2 2 2 2 2 30 15 3 2 y x x x x (3) (b) Hence determine the Maclaurin series expansion for y, in ascending powers of x, up to an
- June 2025, Further Pure 1, Q6 (11 marks): (i) Use L’Hospital’s Rule to show that lim cos sin x x x x 0 1 7 9 49 18 (4) (ii) y = x 2e 3x (a) Use Leibnitz’s theorem to show that, for k ∈ d d e k k k x y
- June 2024, Further Pure 1, Q3 (6 marks): Use L’Hospital’s rule to show that lim sin x x x 0 1 1 0 (6)
- June 2023, Further Pure 1, Q6 (12 marks): y = ln(e 2x cos 3x) – 1 2 < x < 1 2 (a) Show that d d y x x 2 3 3 tan (2) (b) Determine d d 4 4 y x (3) (c) Hence determine the first 3 non-zero terms in ascend
- June 2022, Further Pure 1, Q8 (10 marks): 2 ( ) f ( ) ( ) f ( ) f ( ) ( )f ( ) f ( ) ( ! ( f ) ) 2! = − − = + − + + + + ′ ′′ … … r r The Taylor series expansion of x about x a is giv
- November 2021, Further Pure 1, Q6 (12 marks): 2 ( ) f ( ) ( ) f ( ) f ( ) ( )f ( ) f ( ) ( ! ( f ) ) 2! = − − = + − + + + + ′ ′′ … … r r The Taylor series expansion of x about x a is giv
- November 2020, Further Pure 1, Q1 (5 marks): Use l’Hospital’s Rule to show that 2 sin (e cos(3 ) e) 3 lim tan(2 ) 2 π x x x x → − − = − (5)
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